期刊
COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 352, 期 1, 页码 37-58出版社
SPRINGER
DOI: 10.1007/s00220-016-2778-5
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资金
- Swiss National Science Foundation (SNSF) via the National Centre of Competence in Research QSIT
- European Commission via the project RAQUEL
- SNSF through a fellowship
- Institute for Quantum Information and Matter (IQIM)
- NSF Physics Frontiers Center [PHY-1125565]
- Gordon and Betty Moore Foundation [GBMF-12500028]
- ARO grant for Research on Quantum Algorithms at the IQIM [W911NF-12-1-0521]
- ARC Discovery Early Career Researcher Award (DECRA) fellowship
- ARC Centre of Excellence for Engineered Quantum Systems (EQUS)
We prove several trace inequalities that extend the Golden-Thompson and the Araki-Lieb-Thirring inequality to arbitrarily many matrices. In particular, we strengthen Lieb's triple matrix inequality. As an example application of our four matrix extension of the Golden-Thompson inequality, we prove remainder terms for the monotonicity of the quantum relative entropy and strong sub-additivity of the von Neumann entropy in terms of recoverability. We find the first explicit remainder terms that are tight in the commutative case. Our proofs rely on complex interpolation theory as well as asymptotic spectral pinching, providing a transparent approach to treat generic multivariate trace inequalities.
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